Question: Solve for $x$ and $y$ using elimination. ${2x-5y = -25}$ ${-2x-6y = -74}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $2x$ and $-2x$ cancel out. $-11y = -99$ $\dfrac{-11y}{{-11}} = \dfrac{-99}{{-11}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {2x-5y = -25}\thinspace$ to find $x$ ${2x - 5}{(9)}{= -25}$ $2x-45 = -25$ $2x-45{+45} = -25{+45}$ $2x = 20$ $\dfrac{2x}{{2}} = \dfrac{20}{{2}}$ ${x = 10}$ You can also plug ${y = 9}$ into $\thinspace {-2x-6y = -74}\thinspace$ and get the same answer for $x$ : ${-2x - 6}{(9)}{= -74}$ ${x = 10}$